Contact The Learning Centre

# Exponent Laws & Rules

### Index laws

• Multiplication when the base is the same:
$a^m \times a^n = a^{m+n}$
• Division when the base is the same:
$a^m \div a^n = \frac{a^m}{a^n} = a^{m-n}$
• Power of power rule:
$(a^m)^n = a^{m\times n}$
• Power of a product rule:
$(ab)^m = a^m \times b^m$
• Fractional power notation:
$a^\frac{m}{n} = \sqrt[n]{a^m}$
• The zero index:
$a^0 = 1$
• The negative index:
$a^{-m}= \frac{1}{a^m}$

#### To do

• (sigma Mathematics and Statistics Support Coventry University)